A Concise Representation for the Soft-in Soft-out LMMSE Detector

Abstract

An alternative simple derivation for the well-known soft-in soft-out LMMSE (linear minimum mean square error) detector in a turbo system is presented. The derivation leads to a concise representation for the LMMSE detector in terms of the extrinsic means and extrinsic variances of the data symbols, and provides new perspectives for its implementation.